This phase II trial is studying how well giving cediranib maleate together with combination chemotherapy works in treating patients with advanced biliary cancers. Cediranib maleate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth or by blocking blood flow to the tumor. Drugs used in chemotherapy, such as oxaliplatin, leucovorin calcium, and fluorouracil, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving cediranib maleate together with combination chemotherapy may kill more tumor cells.